Răspuns:
(3ⁿ⁺¹·4+3ⁿ) / (3ⁿ·5+3ⁿ⁺¹)=
[ 3ⁿ·(3·4+1) ]/ [3ⁿ·(5+3)]=
(3ⁿ·13) / (3ⁿ·8)=
13/8
Explicație pas cu pas:
[tex] \dfrac{ 3^{n + 1} \cdot4 +3^{n}}{ 3^{n} \cdot5 +3^{n + 1}} = \dfrac{3^{n} \cdot( 3^{n + 1 - n} \cdot4 +3^{n - n})}{ 3^{n} \cdot(3^{n - n}\cdot5 +3^{n + 1 - n}) } = [/tex]
[tex] \dfrac{3^{n} \cdot( 3^{1 } \cdot4 +3^{0})}{ 3^{n} \cdot(3^{0}\cdot5 +3^{1}) } = \dfrac{ \not3^{n} \cdot( 3 \cdot4 +1)}{ \not 3^{n} \cdot(1\cdot5 +3) } = [/tex]
[tex] = \dfrac{12 +1}{ 5 +3 } = \red{ \boxed{\dfrac{13}{8}}}[/tex]